Waec Model Questions Vol1 2021 Geography Question 1

A farmer plans to grow maize on a hectare of land. The base yield is 2.5 tonnes/ha when 100 kg of nitrogen fertilizer per hectare, 800 mm of rainfall and a planting density of 40 000 plants/ha are used. Yield responses are as follows: each additional 10 kg N (up to a maximum of 150 kg N) adds 0.2 t/ha; each extra 100 mm of rainfall above 800 mm adds 0.1 t/ha (proportionally for other amounts); for every 5 000 plants/ha above the optimal density the yield falls by 0.15 t/ha (no penalty for lower densities). The forecasted rainfall for the season is 950 mm and the farmer can apply at most 150 kg N/ha. Planting density must be an integer multiple of 5 000 plants/ha between 30 000 and 55 000 plants/ha. The selling price of maize is ₦200 000 per tonne. Pest‑control costs ₦15 000 per ha regardless of other inputs and seed costs ₦0.5 per plant. What planting density (plants per hectare) will give the maximum profit and what is that profit (in Naira) per hectare?